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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function ROT = createRotationVector3d(A,B)
%CREATEROTATIONVECTOR3D Calculates the rotation between two vectors.
%
% ROT = createRotationVector3d(A, B) returns the 4x4 rotation matrix ROT
% to transform vector A in the same direction as vector B.
%
% Example
% A=[ .1 .2 .3];
% B=-1+2.*rand(1,3);
% ROT = createRotationVector3d(A,B);
% C = transformVector3d(A,ROT);
% figure('color','w'); hold on; view(3)
% O=[0 0 0];
% drawVector3d(O, A,'r');
% drawVector3d(O, B,'g');
% drawVector3d(O, C,'r');
%
% See also
% transformPoint3d, createRotationOx, createRotationOy, createRotationOz
%
% Source
% https://math.stackexchange.com/a/897677
% ------
% Author: oqilipo
% E-mail: N/A
% Created: 2017-08-07
% Copyright 2017-2023
if isParallel3d(A,B)
if A*B'>0
ROT = eye(4);
else
ROT = -1*eye(4); ROT(end)=1;
end
else
a=normalizeVector3d(A);
b=normalizeVector3d(B);
a=reshape(a,3,1);
b=reshape(b,3,1);
v = cross(a,b);
ssc = [0 -v(3) v(2); v(3) 0 -v(1); -v(2) v(1) 0];
ROT = eye(3) + ssc + ssc^2*(1-dot(a,b))/(norm(v))^2;
ROT = [ROT, [0;0;0]; 0 0 0 1];
end
end
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